Rhyme has been out of fashion in poetry since it was ceded to songwriters. And with good reason, I believe. Cole Porter was as good as they come but he was no poet, even with his bees and educated fleas. I submit he had the music but not the concision and imaginative leaps.
To be sure there are still formalists in our midst. Donald Justice and Richard Wilbur are two highly respected ones. But most contemporary poets are not likely to be seen with a rhyming dictionary. End-rhymes went out with other rigid structures such as sonnets and heroic couplets. It may be the same reason why we don't wear suits and ties on airplanes and so much music is atonal.
Most of us regard Walt Whitman as our antecedent, followed perhaps by Wallace Stevens,
William Carlos Williams and Allen Ginsberg. All of them wrote in free verse.
Ironically the art of poetry has a paucity of words to distinguish its many varieties. That word "verse" is itself a term now consigned to greeting cards. Rhyming poetry is more often associated with doggerel. Indeed poetry has many permutations and they all go under the name, "poetry."
Why has rhyme fallen out of favor? I think because life itself doesn't rhyme. Our experience is
fractured, simultaneous and asymmetric. In fact rhyming lines are devoutly to be avoided by many in favor of assonance or alliteration in a limited way. Rhymes carry the whiff of levity or constricted artifact.
There is an argument that the imposition of a rhyming right-hand margin forces the poet to stretch his imagination but too often it compromises language to obey the prescribed form.
It's fair to say, however, that much poetry is moving to performance as it seeks it's roots in the oral tradition. Thus we have rap music/poetry and a return to rhyme. Putting this aside I am speaking for the poem on the page.
Freedom isn't license but poetic license makes its own demands; to cultivate one's own authentic voice without affectation and alert to the limp and bloated language all around us.
It was either I or William Stafford who once remarked that all words rhyme with each other more so than they do with silence. With this mind, as a concession to the rhymers of the world, I offer the following:
All words rhyme with each other
more than the winds and the weather
but I prefer a B-flat
from the wings of a gnat
to the marriage of mother to brother.